Fluctuation theorems and 1/f noise from a simple matrix

Here we present a model for a small system combined with an explicit entropy bath that iscomparably small. The dynamics of the model is defined by a simple matrix, M. Each row ofM corresponds to a macrostate of the system, e.g. net alignment, while the elements in therow represent microstates. The constant number of elements in each row ensures constantentropy, which allows reversible fluctuations, similar to information theory where aconstant number of bits allows reversible computations. Many elements in M come from themicrostates of the system, but many others come from the bath. Bypassing the bath statesyields fluctuations that exhibit standard white noise; whereas with bath states the powerspectral density varies as S(f) ∝ 1 /f overa wide range of frequencies, f. Thus, the explicit entropy bath is the mechanismof 1/f noisein this model. Both forms of the model match Crooks’ fluctuation theorem exactly,indicating that the theorem applies not only to infinite reservoirs, but also tofinite-sized baths. The model is used to analyze measurements of 1/f-like noise from asub-micron tunnel junction.     

Preparation of polysiloxanes from silicic acid. V. Condensation of silicic acid butyl esters and formation of silica fiber from the ester solutions

The condensation of silicic acid butyl esters was investigated by gel permeation chromatographic (GPC) analysis. The results revealed that the condensation was greatly dependent on a degree of esterification of the esters. The ester with the lowest degree of esterification underwent condensation to form a highly polymerized ester. It was found that fibers could be drawn from the ester solution before gelation.     

Scandium(III) trifluoromethanesulfonate catalyzed aromatic nitration with inorganic nitrates and acetic anhydride

The rare earth metal(III) trifluoromethanesulfonate (rare earth metal(III) triflate, RE(OTf)3) was found to be an efficient catalyst for aromatic nitration with carboxylic anhydride-inorganic nitrate as the nitrating agent. In the presence of a catalytic amount of RE(OTf)3, the nitration of substituted benzenes proceeded to afford the corresponding nitrobenzenes. Especially, scandium(III) trifluoromethanesulfonate (scandium(III) triflate, Sc(OTf)3) is the most active catalyst among our tested Lewis acids. It was also found that acetic anhydride-Al(NO3).9H2O is the most active nitrating agent in this system.     

PHENYLATION OF PYRIDINE BY PHOTOLYSIS OF DIPHENYL SULFONE

Abstract

The photolysis of diphenyl sulfone in neat pyridine or pyridine diluted with the organic solvent, with a high-pressure mercury arc lamp, was studied. The presence of acetone in the reaction system remarkably promoted photochemical conversion of the sulfone. The isomer distribution ratios (β > α > γ) of phenylpyridines produced during the reaction were clearly different from those (α > β > γ) so far reported for a free-radical phenylation of pyridine. Benzenesulfinic acid produced in the reaction was separated from the product mixture and identified as its S-benzylthiuronium derivative.     

π–π Stacking Interaction in an Oxidized CuII–Salen Complex with a Side-Chain Indole Ring: An Approach to the Function of the Tryptophan in the Active Site of Galactose Oxidase

In order to gain new insights into the effect of the π–π stacking interaction of the indole ring with the Cu^II–phenoxyl radical as seen in the active form of galactose oxidase, we have prepared a Cu^II complex of a methoxy-substituted salen-type ligand, containing a pendent indole ring on the dinitrogen chelate backbone, and characterized its one-electron-oxidized forms. The X-ray crystal structures of the oxidized Cu^II complex exhibited the π–π stacking interaction of the indole ring mainly with one of the two phenolate moieties. The phenolate moiety in close contact with the indole moiety showed the characteristic phenoxyl radical structural features, indicating that the indole ring favors the π–π stacking interaction with the phenoxyl radical. The UV/Vis/NIR spectra of the oxidized Cu^II complex with the pendent indole ring was significantly different from those of the complex without the side-chain indole ring, and the absorption and CD spectra exhibited a solvent dependence, which is in line with the phenoxyl radical–indole stacking interaction in solution. The other physicochemical results and theoretical calculations strongly support that the indole ring, as an electron donor, stabilizes the phenoxyl radical by the π–π stacking interaction.     

Mechanism of an alcohol-trapping reaction in the direct and benzophenone-sensitized photodenitrogenation of a spiroepoxy-substituted azoalkane: solvent effects and stereochemical deuterium labeling

The spin-state-dependent reactivity, singlet versus triplet, of the 2-spiroepoxy-1,3-cyclopentane-1,3-diyl DR2 has been assessed through alcohol-trapping reactions for which the effect of solvent acidity on the product distribution of the alcohol trapping products 2 versus 3 + 4 and stereochemical deuterium-labeling studies have been performed. The proposed mechanism for the solvent effect on the product ratio (2/3 + 4) reveals the importance of the hydrogen-bonded intermediates I1 and I2 in the trapping reactions; the stereochemical deuterium-labeling results clarify the dipole structure trapped by the alcohol. The dipoles DP1 and DP2, in which the configuration between the epoxide oxygen and the deuterium atoms is retained, are inferred for the direct photodenitrogenation reactions (singlet state), whereas for the benzophenone-sensitized photoreactions (triplet state), after ISC, the ring-opened dipole DP3 is implied as the intermediate that is trapped by the alcohol.     

Kinetic determination of trace cobalt(II) by visual autocatalytic indication

A highly sensitive and simple visual autocatalytic method has been developed for the determination of trace cobalt. The cobalt ion released by the oxidative decomposition of inert bis[2-(5-bromo-2-pyridylazo)-5-(N-propyl-N-sulfopropyl-amino-phenolato] cobaltate (Co(III)-5-Br-PAPS) with peroxomonosulfate acts as a catalyst for the oxidative degradation of the complex. Thus a definite time lapse of degradation is observed by the sudden disappearance of colored Co(III) complexes. The degradation time varies inversely with the logarithm of the initial concentration of cobalt(II). The determination range of cobalt(II) was from 3x10(-9) to 2x10(-7) M in the presence of 5x10(-6) M of 5-Br-PAPS. The relative standard deviation of the spot size method (10 mul) was 3.5% at 1x10(-7) M cobalt(II). This autocatalytic indicator reaction system has been successfully applied for the visual determination of urinary cobalt.     

Organometallic Rotaxanes with a Triazole Group in the Axle Component and Their Behavior as Ligands of PtII Complexes

Two ferrocenylmethyl ammonium salts were used as axle components of pseudorotaxanes with dibenzo[24]crown‐8. The pseudorotaxane with an alkyne terminal group in the axle component underwent a Cu‐catalyzed Huisgen coupling reaction (click reaction) with an alkyl azide to afford cationic [2]rotaxanes with a triazole group in the axle molecule. The rotaxane reacted with Ac₂O to produce neutral rotaxanes with an amide group in the axle component. Both cationic and neutral rotaxanes were treated with K[PtCl₃(CH₂?CH₂)] to form the Pt^II‐containing rotaxanes.